Question

What is the distance between `(7,5,-6)` and `(-1,6,3)`?

Answer 1

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

`d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)`

Substituting the values from the points in the problem gives:

`d = sqrt((color(red)(-1) - color(blue)(7))^2 + (color(red)(6) - color(blue)(5))^2 + (color(red)(3) - color(blue)(-6))^2)`

`d = sqrt((color(red)(-1) - color(blue)(7))^2 + (color(red)(6) - color(blue)(5))^2 + (color(red)(3) + color(blue)(6))^2)`

`d = sqrt((-8)^2 + 1^2 + 9^2)`

`d = sqrt(64 + 1 + 81)`

`d = sqrt(146)`

Or

`d ~= 12.083`